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24 Cards in this Set
- Front
- Back
- 3rd side (hint)
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THE 5 KEY WORDS OF COMPETENACY 13
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PATTERNS
SEQUUENCES ALGEBRIAC MANIPULAITON FUNCTION MULTIPLE REPRESENTAION |
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A F M |
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FIRST OF COMP 13 DESCRIPTOR HIGHLIHTSOF THIS COMPETENC
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THE ESSENCE OF THIS COMPETENCY IS TO BE ABLE TO MOVE FROM ONE MODE OF REPRESENTATION FOR SEQUENCES AND FUNCTIONS
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TO MOVE TO A NEW MODE
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SECOND OF COMP 13 DESCRIPTOR HIGHLIHTSOF THIS COMPETENCY
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FOR VARIABLES, EXPRESSIONS, EQUATIONS, INEQUALITIES RELATIONS AND FUNCTIONS=THE FOCUS IS ON THE RELTIONSHIPS AMONG THEM
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THE FOCUS IS ON THE RELAITONSHIPS
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COMP 13-PATTERNS USING MULTIPLE REPRESENTATIONS-GIVE AN EXAMPLE OF A CONCRETE VISUAL MODEL
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SOMETHING LIKE A TRIANGLE WITH THREE LITTLE TRIANGLES POINTED TO EACH OTHER ON THE INSIDE-PREDICT THE NUMBER OF
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PREDICT THE NUMBER OF TRIANGLES IN THE NEXT TWO LAYERS-
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eXTEND THE SIDES OF THE TRIANGLE AND THE LINES PARALLEL TO THEM TO DRAW THE NEXT TWO LAYERS
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PREDICT THE NUMBER OF TRIANGLES AND THE PARALLEL TO THEM TO DRAW THE NEXT TWO LAYERS
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PATTERNS INVOLVING REPRESENTAION-TABLE
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NUMBOFTRMS|PROC.COLUMN|TERM
1 | 1 PLUS 0 }1 2 } 2+1 }3 3 } 3+2 } 5 4 | 4+3 | 7 5 | 5+4 | 9 N | N+N-1 |
DO YOU UNDERSTAND THE LAST PART OF THE TABLE
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THE BASIC GRAPH
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RISE/RUN
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VERBAL DESCRIPTION
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value of the ter=two times the term number minus one
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ALGEBRAIC EXPRESSIONS
MAKE A PROCESS COLUMN |
WRITE AN ALGEBRA FORMULA USING N AS THE TERM NUMBER TO PREDICT THE VALUE OF ANY TERM IN A SEQUENCE: iF YOU BUILD A PROCESS COULUMN, YOU CAN DETERIMINE THE FORMULA MORE EASILY f(n)=2n-1
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iF YOU BUILD A PROCESS COULUMN, YOU CAN DETERIMINE THE FORMULA MORE EASILY f(n)=2n-1
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YOU CAN USE SEQUENCES OF MULTIPLE REPRESENTATIONS HOW
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THE SEQUENCE CAN BE GEERATED FROM ANY OF THE REPRESENTATIONS YOU CAN START AT ANY ONE OF THE REPRESENTATIONS AND MOVE TO THE NEXT ONE.
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FUCTIONS USING MULTIPLE REPRESENTATIONS-DEFINE A FUNCTION
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A SET OF POINTS (X,Y) WITH EXACTLY ONE DISCTINCT VALUE OF Y FOR EVERY VALUE OF X
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DEFINE A FUNCTION
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FUCTIONS USING MULTIPLE REPRESENTATIONS-NAME THE 5 MODES OF REPRESENT
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VERBAL
PICTORIAL TABULAR GRAPHICAL SYMBOLIC |
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P T G S |
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FUCTIONS USING MULTIPLE REPRESENTATIONS-VERBAL EXAMPLE
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A COUPLE IS PLAINNING TO PUT A RUG IN ONE CORNER OF THEIR FAMILY ROOM, LEAVING A STRIP OF FLOOR THE SAME WIDTH ON TWO SIDES OF THE ROOM. THE DIMENSIONS OF THE ROOM ARE 4 METES BY 6 METERS, WRITE AN EXPRESSION TO REPRESENT THIS FUCTION
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VERBAL
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FUCTIONS USING MULTIPLE REPRESENTATIONS-PICTORIAL
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A SQUARE SHAPE WITH 6 METERS ON TOP>>>>>>>>>>>>
4 METERS AS THE WIDTHE |
PICTORIAL
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FUCTIONS USING MULTIPLE REPRESENTATIONS-TABULAR
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W OF |LENGTH|WIDTH| AREA
UNCARPET | STRIP LOOK AT PAGE 56 OF FLOOR 0 6 4 24 1 5 3 15 |
TABULAR
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FUCTIONS USING MULTIPLE REPRESENTATIONS-GRAPHIC
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THE AREA (0 TO 24)WOULD BE ON THE Y AXIS A(0,10) AND THE WIDTH OF UNCARPETED PEOPLE
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GRAPHIC
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FUCTIONS USING MULTIPLE REPRESENTATIONS-SYMBOLIC
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X=WIDTH OF UNCARPTETED FLOOR
F(X)=(6-X)(4-X) |
SYMBOLIC
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OPERATIONS ON MULTIPLICATION, COEFFICIENTS, MULTIPLY VARIABLES
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7X(X-3)=7X^2-21X
(2X-1)(X+2)=2X^2+4X-X-2=2X^2+3X-2 |
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OPERATIONS ON MULTIPLICATION, COEFFICIENTS-dIVISION: FACTOR AND REDUCE-EXAMPLES
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12X-6/6+ 6(X-2)=(X-2)
X^2+7X+6/(X+6)(X+1)/X+1=(X+6)[ |
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OPERATIONS ON MULTIPLICATION, COEFFICIENTS, MULTIPLY VARIABLES-INEQUALITIES
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SINGLE INEQUALITIES: ONLY ONE INEQUALITY SIGN DIVIDED/MULTIPLIED BY A NEGATIVE NUMBER THE INEQUALITY IS REVERSED
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EXAMPLES OF INEQUALITES
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5X+8<(LESS THEN OR EQUAL TWO) 8X =14
-3X+8<(LESSTHAN OR EQUAL TO-3X < ( LESS THAN OR EQUAL TO X>(GTOET) -2 **DIRECTION OF INEQUALITY REVERSES DUE TO DIVISION BY A NEGATIVE |
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INQUALITIES_EXAMPLE 1
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IN 2004 AAA ESTIMATED THAT THE COSE OF OPERATING A NEW FORD TAURUS WAS .71 CENTS A MILE.
tHIS DID NOT INCLUDE TEH CAR PAYMENT. SELECT THE INEQUALITY THAT REPRESENTS TOTAL CAR EXPENSES OF $700 TO 1000.00 PER MONTH, INCLUDING A CAR PAYMETN, IF M TO REPRESENTS THE AVERAGE NUMBER OF MILES TRAVLED IN A MONTH AND P REPRESENTS THE AVERAGE NUMBER OF MILES TRAVELED IN A MONTH AND P REPRESENTS THE MONTHLY CAR PAYMENT B. 700<(LTOE).71M+P< (LTOE) 1000 REMEMEBER THAT YOUR MONEY EXPRESSIONS MUST BE THE SAME DENOMINATIONS -CHANGE THE 71 CENTS TO .71 SO IT IS EXPRESSED IN DOLLRS -THE CAR PAYMENT REMAINS THE SAME CONSTANT EACH MONTH AND THE UPSKEEP COST CHANGE DEPENDS ON MILAGE DRIVE |
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using the SEQUENCE BELOW, CONTINE TO GENERATE A DESCRIPTION OF THE PROCESS FO RDETERMING THE SUM OF THE INTERIOR ANGLES OF A POLYGON IN TERMS OF THE NUMBBER OF SIDES OF A POLYGON:
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THE SHAPES WRITTEN OUT AND NOT SHOWN: A REGULAR TRIANGLE, A SQUARE WITH THE LINE ON THE SIDE, A POLYGON WITH A SMALLER BROKEN LINE TRIANGLE ON THE INSIDE, THEN TWO MORE POLYGONS TO THE RIGHT
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**PROBLEM OF UNDERSTANDING
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RDETERMING THE SUM OF THE INTERIOR ANGLES OF A POLYGON IN TERMS OF THE NUMBBER OF SIDES OF A POLYGON:
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C) THE SUM OF THE INTERIOR ANGLES OF A POLYGON IS EQUAL TO =180 DEG. * THE NUMBER OF SIDES MINUS TWO)
THIS IS A PATTERN WITH A PATTERN PROBLEM. DRAW IN TEH DIAGONALS FOR THE LAST 2 POLYGONS. lOOK AT THE NUMBER OF TRIANGLES IN EACH POLYGON AND DETERMINE HOW THIS IS RELATED TO THE NUMBER OF SIDES. RECALL THAT TEH SUM OF THE ANGLES OF A TRIANGLE IS 180 DEG. ***RECALL THAT THE SUM OF THE ANGLES OF A TRIANGLE IS 180 DEG. SO THE SUM OF THE ANGLES OF NAY POLYGON IS THE NUMBER OF TRIANGLES FORMED BY A DIAGOANLF FROM ONE VERTEX TIMES 180 DEGREES. uSING THE NUMBER OF SIDES OF THE POLYGON THIS WOULD BE A THE THE (NUMBER OF SIDES - 2 *180 DEGREES) |
IF YOU ARE COMF. YOU MAY WANT TO PUT IN FORMULA FORM
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